Dynamic AdS/QCD and the spectra of gauge theories Nick Evans University of Southampton New understanding of holographic descriptions of mesons A stab at predicting the spectra of arbitrary AF gauge theories Oxford October 2014
Back track to 2005 Top down models of chiral symmetry breaking Bottom up AdS/QCD
Building Holographic QCD
Orthonormal wave functions
Add Confinement and Chiral Symmetry Breaking Dilaton Flow Geometry: Gubser, Sfetsos Here, this is just a simple, back reacted, repulsive, hard wall…. Babington et al, Ghoroku..
Erdmenger, NE,Kirsch, Threlfall 0711.4467 These models live at very large coupling – QCD is at intermediate coupling strength… The running coupling is rather different (UV strong fixed point) Success beyond caricature seems surprising… how does one improve towards QCD?
Back track to 2005 Top down models of chiral symmetry breaking Bottom up AdS/QCD
Son, Stephanov, Traditional AdS/QCD Erlich, Katz Parameter count r o c = qq m g 5
The basic ideas are remarkably good… but… to systematically move to QCD we would need to: IR improve – include all operators that are non-zero in the vacuum and back react them on each other UV perfect – need to match the running of operators to the true perturbative QCD values in the UV…. No dynamics – inputing condensate and hard wall and fitting is only dynamics…. Of course as in any effective description of QCD this is overwhelming and you end up just re- parameterizing the data…. In QCD the regime of validity of the gravity description is very tight …
A New Insight in 2012 It had been quite hard to understand how to put in the dynamics of an individual gauge theory…
Holographic Models for QCD in the Veneziano Limit Matti Jarvinen, Elias Kiritsis 1112.1261 We model the qq condensate by a scalar in “ AdS ”… Breitenlohner-Freedman Bound A scalar in AdS is stable until msq < - 4 ie D < 2 A hard prediction that matches gap equation-ology for the on-set of chiral symmetry breaking… Holographic models work for QCD mesons because they are describing the running of the anomalous dimension of qq rather than the running of the coupling…
Alvares, NE, Kim, D3/ Probe D7 Model 1204.2474 l This is the action of a scalar in AdS with a mass squared of -3 + r dependent correction from the gradient of l
For example if we try to (very naively) input the two loop QCD running of the coupling… l Nf/Nc = 3.. 4.5 m We output these running masses… to be compared with the perturbative expectation below…
Top-down probe-brane models of QCD are just AdS/QCD with the background providing a running g …
Dynamic AdS/QCD Timo Alho, NE, KimmoTuominen 1307.4896 D7 probe action in AdS expanded to quadratic order X is now a dynamical field whose solution will determine the condensate as a function of m We use the top-down IR boundary condition on mass- shell: X’( r =X) = 0 X enters into the AdS metric to cut off the radial scale at the value of m or the condensate – no hard wall The gauge DYNAMICS is input through D m The only free parameters are Nc, Nf, m, L
Formation of the Chiral Condensate We solve for the vacuum configuration of L L Shoot out Nc=3, Nf=9 Read off m with and qq in the UV… L’( r =L) = 0 r Now solve for meson masses by looking at linearized fluctuations about this vacuum…
Quenched SU(Nc) gauge NE, Erdmenger & Mark Scott Lattice data high due to extrapolation? M_rho = 1 defines L Real QCD lies here There is very little Nc dependence Comparison to quenched lattice data (Bali et al… arXiv1304.4437) All of these models lie within 10% on any point....
Quenched SU(Nc) gauge M_rho = M_pi
SU(3) gauge theory + Nf quarks M_rho = 1 defines L Real QCD lies here M_rho = M_pi
SU(3) gauge theory + Nf quarks We do see new behaviour as Nf heads towards 12….
The Conformal Window SU(Nc) gauge theory with Nf fundamental quarks No AF Nf=11/2 Nc CFT Nf = 4 Nc c SB l Nf/Nc = 3.. 4.5 m If critical g = 1…. Nf/Nc ~ 4 m Yamawaki,Appelquist, Terning, Sannino ,…
Walking Dynamics Holdom Just above the CW regime theories have an enhanced UV quark condensate • Is the sigma particle light – a techni-dilaton? • Is the higgs such a technicolor state?
SU(3) gauge theory + Nf quarks The QCD point is not right for the f0(500) but about right for the f0(980) – is the f0(500) odd eg a molecule ??? We indeed see a light sigma relative to the rho…
Alho, NE, Tuominen 1307.4896 qq enhancement reproduced…. Cf FCNC problem in TC
Pick your theory… Input (assumed) running of g for any theory you fancy… eg SU(3) gauge +
Glueballs The model concentrates on the quark states… we’re not trying to describe the running of the coupling or Tr F^2… however for us roughly… Find the dynamical IR quark mass… below that scale run the coupling as pure YM.. Find the IR pole… multiply by 8 and that’s the glueball mass! SU(3) Nf=3
SU(3) Nf=3 SU(3) Nf=11
Study the Conformal Window NE, Scott 1405.5373 For Nf > 4 Nc there is no dynamical scale so study the theory at non- zero quark mass… eg SU(3) gauge + 13 flavours b=1 for the conformal IR and UV regimes but deviates at the intermediate running scale…
Conclusions Holographic models of QCD continue to improve… running of g is crucial…one gets a good description of the lowest lying spectra at better than 10% and you can see generic behaviours with Nc Nf easily... Holography is a remarkably simple method to get a ball park answer for behaviour… but it still can’t be systematically improved… Hopefully Models are useful to guide lattice practitioners… On going work: T m phase structure… pomeron physics… enlarging to the full QCD spectra… why can I ignore other operators?
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